• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.643-647
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• 2013

Let G be a group and let $p$ be a prime number. If the set $\mathcal{A}(G)$ of all commuting automorphisms of G forms a subgroup of Aut(G), then G is called $\mathcal{A}(G)$-group. In this paper we show that any $p$-group with cyclic maximal subgroup is an $\mathcal{A}(G)$-group. We also find the structure of the group $\mathcal{A}(G)$ and we show that $\mathcal{A}(G)=Aut_c(G)$. Moreover, we prove that for any prime $p$ and all integers $n{\geq}3$, there exists a non-abelian $\mathcal{A}(G)$-group of order $p^n$ in which $\mathcal{A}(G)=Aut_c(G)$. If $p$ > 2, then $\mathcal{A}(G)={\cong}\mathbb{Z}_p{\times}\mathbb{Z}_{p^{n-2}}$ and if $p=2$, then $\mathcal{A}(G)={\cong}\mathbb{Z}_2{\times}\mathbb{Z}_2{\times}\mathbb{Z}_{2^{n-3}}$ or $\mathbb{Z}_2{\times}\mathbb{Z}_2$.

• Korean Journal of Pharmacognosy
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• v.31 no.1
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• pp.95-100
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• 2000

In order to find out hypoglycemic constituents from natural resources, Korean medicinal plants being used for the treatments of diabetes mellitus were tested with streptozotocin-induced diabetic rats. From the above screening, the $CH_2Cl_2$ fraction of 80% methanol extracts of Morus alba leaves showed hypoglycemic activity. The $CH_2Cl_2$fraction was chromatographed on silica gel, resulting in 9 subfractions, and tested hypoglycemic activity. The subfraction which had a strong hypoglycemic activity was rechromatographed and two galactolipids (compounds 1 and 2) were isolated along with a triterpene (compound 3) from other fractions. On the basis of spectroscopic data, acid hydrolysis, alkaline hydrolysis and enzyme hydrolysis results, compounds 1, 2 and 3 were identified as $1-O-(9Z,12Z,15Z-octatrienoyl)-2-O-(9Z,12Z,15Z-octatrienoyl)-3-O-{\beta}-D-galactopyranosyl$ glycerol, $2(R)-1-O-octadecanoyl-2-O-(9Z,12Z,15Z-octatrienoyl)-3-O-{\beta}-D-galactopyranosyl$ glycerol, and $3{\beta}-hydroxylup-20(29)-ene$ acetate, respectively. Compound 2 (1mg/kg p.o.) has approximately 16% hypoglycemic activity in streptozotocin-induced diabetic rats.

• YAKHAK HOEJI
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• v.37 no.3
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• pp.295-305
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• 1993

In order to develop oral cephalosporin having a new substituent at 3 position, the synthesis of cephalosporins modified at C-3 and the effect of the substituents on the oral absorption is studied. 7-[(Z)-2-(2-Aminothiazole- 4-yl)-2-methoxyiminoacetamidol-3-[4-(2-pyridyl )piperazinyl] thiocarbonylthiomethyl-3-cephem-4-carboxylic acid (CEN1) and 7-[(Z)-2-(2-aminothiazole-4-yl)-2-methoxyiminoacetamido]-3-[4-(2-pyrimid yl)piperazinylthiocarbonylthiomethyl-3-cephem-4-carboxylic acid (CEN2) were synthesized from 4-(2-piridyl)piperazinyl dithiocarbamate potassium salt or 4-(2-pirimidyl)piperazinyl dithiocarbamate potassium salt and cefotaxime. Also pivaloyloxymethyl esters of CEN1 and CEN2, pivaloyloxymethyl 7-[(Z)-2-(2-aminothiazole-4-yl)-2-methoxyiminoacetamido]-3-[4-(2-pyridyl )piperazinyllthiocarbonylthiomethyl-3-cephem-4-carboxylate (CENIP) and pivaloyloxymethyl 7-[(Z)-2-(2-aminothiazole-4-yl)-2-methoxyiminoacetamidol-3- [4-(2-pyrimid yl)piperazinyllthiocarbonylthiomethyl-3-cephem-4-carboxylate (CEN2P) were synthesized. The in vitro activities of two new oral cephalosporins, CEN1 and CEN2, were compared with the in vitro activities of cefaclor and cefotaxime against a variety of bacterial species. CEN2 has a broad antibacterial spectrum covering Gram-positive and Gram-negative bacteria, similar to that exhibited by CEN1 and cefotaxime. CEN1 and CEN2 were more active in vitro than cefaclor against Streptococcus pyogenes, Klebsiella aerogenes and Enterobacter cloacae.

• Communications of the Korean Mathematical Society
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• v.19 no.3
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• pp.507-517
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• 2004

Let (2,2,2,2) be ramification indices for the Riemann sphere. It is well known that the regular branched covering map corresponding to this, is the Weierstrass P function. Lattes [7] gives a rational function R(z)= ${\frac{z^4+{\frac{1}{2}}g2^{z}^2+{\frac{1}{16}}g{\frac{2}{2}}$ which is chaotic on ${\bar{C}}$ and is induced by the Weierstrass P function and the linear map L(z) = 2z on complex plane C. It is also known that there exist regular branched covering maps from $T^2$ onto ${\bar{C}}$ if and only if the ramification indices are (2,2,2,2), (2,4,4), (2,3,6) and (3,3,3), by the Riemann-Hurwitz formula. In this paper we will construct regular branched covering maps corresponding to the ramification indices (2,4,4), (2,3,6) and (3,3,3), as well as chaotic maps induced by these regular branched covering maps.

• Journal of the Korean Chemical Society
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• v.19 no.4
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• pp.240-245
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• 1975

Substituent effects of benzyl substrates for the reaction of substituted benzyl(Z) arenesulfonate(X) with dimethylanilines in (Y) acetone at $35^{circ}$ were studied. The interactions between Z and Y disappeared when changed from electron withdrawing group to releasing group in benzyl substrates. The disappearance of interactions between Z and Y infers change of mechanism from $S_N2 to S_N1$ in substituent Z.

• 한국전기화학회:학술대회논문집
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• 2001.10a
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• pp.33-33
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• 2001

• Journal of the Chungcheong Mathematical Society
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• v.19 no.2
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• pp.189-196
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• 2006

The generalized Hyers-Ulam stability problems of the cubic functional equation f(x + y + z) + f(x + y - z) + 2f(x - y) + 4f(y) = f(x - y + z) + f(x - y - z) +2f(x + y) + 2f(y + z) + 2f(y - z) shall be treated under the approximately odd condition and the behavior of the cubic mappings and the additive mappings shall be investigated. The generalized Hyers-Ulam stability problem for functional equations had been posed by Th.M. Rassias and J. Tabor [7] in 1992.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.1937-1943
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• 2015

For $1{\leq}{\alpha}<2$, let $\mathcal{F}({\alpha})$ denote the class of locally univalent normalized analytic functions $f(z)=z+{\Sigma}_{n=2}^{\infty}{a_nz^n}$ in the unit disk ${\mathbb{D}}=\{z{\in}{\mathbb{C}}:{\left|z\right|}<1\}$ satisfying the condition $Re\(1+{\frac{zf^{{\prime}{\prime}}(z)}{f^{\prime}(z)}}\)>{\frac{{\alpha}}{2}}-1$. In the present paper, we shall obtain the sharp upper bound for Fekete-$Szeg{\ddot{o}}$ functional $|a_3-{\lambda}a_2^2|$ for the complex parameter ${\lambda}$.

• Nonlinear Functional Analysis and Applications
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• v.29 no.3
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• pp.621-633
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• 2024

Let R_n be the space of rational functions with prescribed poles. If r ∈ R_n, does not vanish in |z| < k, then for k = 1 $${\mid}r^{\prime}(z){\mid}{\leq}{\frac{{\mid}B^{\prime}(z){\mid}}{2}}\sup_{z{\in}T}{\mid}r(z){\mid}$$, where B(z) is the Blaschke product. In this paper, we consider a more general class of rational functions rof ∈ R_m*n, defined by (rof)(z) = r(f(z)), where f(z) is a polynomial of degree m^* and prove a more general result of the above inequality for k > 1. We also prove that $$\sup_{z{\in}T}\left[\left|{\frac{r^{*\prime}(f(z)}{B^{\prime}(z)}}\right|+\left|{\frac{r^{\prime}(f(z))}{B^{\prime}(z)}}\right|\right]=\sup_{z{\in}T}\left|{\frac{(rof)(z)}{f^{\prime}(z)}}\right|$$, and as a consequence of this result, we present a generalization of a theorem of O'Hara and Rodriguez for self-inverse polynomials. Finally, we establish a similar result when supremum is replaced by infimum for a rational function which has all its zeros in the unit circle.

• Restorative Dentistry and Endodontics
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• v.34 no.5
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• pp.450-459
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• 2009

The aim of this study was to measure the initial dynamic modulus changes of light cured composites using a custom made rheometer. The custom made rheometer consisted of 3 parts: (1) a measurement unit of parallel plates made of glass rods, (2) an oscillating shear strain generator with a DC motor and a crank mechanism, (3) a stress measurement device using an electromagnetic torque sensor. This instrument could measure a maximum torque of 2Ncm, and the switch of the light-curing unit was synchronized with the rheometer. Six commercial composite resins [Z-100 (Z1), Z-250 (Z2), Z-350 (Z3), DenFil (DF), Tetric Ceram (TC), and Clearfil AP-X (CF)] were investigated. A dynamic oscillating shear test was undertaken with the rheometer. A certain volume ($14.2\;mm^3$) of composite was loaded between the parallel plates, which were made of glass rods (3 mm in diameter). An oscillating shear strain with a frequency of 6 Hz and amplitude of 0.00579 rad was applied to the specimen and the resultant stress was measured. Data acquisition started simultaneously with light curing, and the changes in visco-elasticity of composites were recorded for 10 seconds. The measurements were repeated 5 times for each composite at $25{\pm}0.5^{\circ}C$. Complex shear modulus G*, storage shear modulus G', loss shear modulus G" were calculated from the measured strain-stress curves. Time to reach the complex modulus G* of 10 MPa was determined. The G* and time to reach the G* of 10 MPa of composites were analyzed with One-way ANOVA and Tukey's test ($\alpha$ = 0.05). The results were as follows. 1. The custom made rheometer in this study reliably measured the initial visco-elastic modulus changes of composites during 10 seconds of light curing. 2. In all composites, the development of complex shear modulus G* had a latent period for $1{\sim}2$ seconds immediately after the start of light curing, and then increased rapidly during 10 seconds. 3. In all composites, the storage shear modulus G" increased steeper than the loss shear modulus G" during 10 seconds of light curing. 4. The complex shear modulus of Z1 was the highest, followed by CF, Z2, Z3, TC and DF the lowest. 5. Z1 was the fastest and DF was the slowest in the time to reach the complex shear modulus of 10 MPa.